次BL代数的修正及其应用

The Simplified Definition and the Equivalent Forms of Sub-BL Algebra

次BL代数是多个重要逻辑代数的理论基础,文章对次BL代数作了进一步的深入研究,得到了一些很好的结论,其主要结果有:1)简化了次BL代数的定义;2)给出了次BL代数的另外两种等价形式,进一步揭示了次BL代数与其他逻辑代数之间的关系;3)证明了一种强次BL代数与BR0代数之间的等价关系,并以次BL代数为基础给出了BR0代数和R0代数的简化定义,改进了已有的结果.

Sub-BL algebra is the basic of many important logical algebras. It is further analyzed and some mature conclusions are obtained in this paper：firstly,the definition of Sub-BL algebra is simplified;secondly,another two equivalent forms of Sub-BL algebra are given out, revealing the real relationship among Sub-BL algebra and other logical algebras; finaly, the equivalence between Sub-BL algebra and BRo algebra is proved, respectively simplifying the definitions of BRo algebra and R0 algebra.